Search Results for author:
Found 30 papers, 10 papers with code
On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution.
NEO: Non Equilibrium Sampling on the Orbits of a Deterministic Transform
Sampling from a complex distribution $\pi$ and approximating its intractable normalizing constant $\mathrm{Z}$ are challenging problems.
Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimension
As a consequence, the same dependence on the step size and the dimension as in the product case can be recovered for several important classes of models.
Monte Carlo Variational Auto-Encoders
Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO).
Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits.
DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbs
Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning.
Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsize
This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system $\bar{A}\theta = \bar{b}$ for which $\bar{A}$ and $\bar{b}$ can only be accessed through random estimates $\{({\bf A}_n, {\bf b}_n): n \in \mathbb{N}^*\}$.
QLSD: Quantised Langevin stochastic dynamics for Bayesian federated learning
The objective of Federated Learning (FL) is to perform statistical inference for data which are decentralised and stored locally on networked clients.
NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform
Sampling from a complex distribution $\pi$ and approximating its intractable normalizing constant Z are challenging problems.
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie
The proposed algorithms are demonstrated on several canonical problems such as image deblurring, inpainting, and denoising, where they are used for point estimation as well as for uncertainty visualisation and quantification.
On Riemannian Stochastic Approximation Schemes with Fixed Step-Size
This result gives rise to a family of stationary distributions indexed by the step-size, which is further shown to converge to a Dirac measure, concentrated at the solution of the problem at hand, as the step-size goes to 0.
On the Stability of Random Matrix Product with Markovian Noise: Application to Linear Stochastic Approximation and TD Learning
This paper studies the exponential stability of random matrix products driven by a general (possibly unbounded) state space Markov chain.
Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees
This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms.
Quantitative Propagation of Chaos for SGD in Wide Neural Networks
In comparison to previous works on the subject, we consider settings in which the sequence of stepsizes in SGD can potentially depend on the number of neurons and the iterations.
Convergence Analysis of Riemannian Stochastic Approximation Schemes
This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems.
Convergence rates and approximation results for SGD and its continuous-time counterpart
This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes.
Statistical and Topological Properties of Sliced Probability Divergences
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base divergence' between one-dimensional random projections of the two measures.
MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference
In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC).
Maximum entropy methods for texture synthesis: theory and practice
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis.
Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part I: Methodology and Experiments
In this work, we propose a general empirical Bayesian method for setting regularisation parameters in imaging problems that are convex w. r. t.
Methodology Computation 62C12, 65C40, 68U10, 62F15, 65J20, 65C60, 65J22
Approximate Bayesian Computation with the Sliced-Wasserstein Distance
Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood.
Markov Decision Process for MOOC users behavioral inference
Studies on massive open online courses (MOOCs) users discuss the existence of typical profiles and their impact on the learning process of the students.
Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance
Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generative modeling (e. g. Wasserstein generative adversarial networks, Wasserstein autoencoders).
Copula-like Variational Inference
This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i. e. with a complexity linear in the dimension of state space.
The promises and pitfalls of Stochastic Gradient Langevin Dynamics
As $N$ becomes large, we show that the SGLD algorithm has an invariant probability measure which significantly departs from the target posterior and behaves like Stochastic Gradient Descent (SGD).
Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions
To the best of our knowledge, the proposed algorithm is the first nonparametric IGM algorithm with explicit theoretical guarantees.
Analysis of Langevin Monte Carlo via convex optimization
In this paper, we provide new insights on the Unadjusted Langevin Algorithm.
Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains
We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size.
Stochastic Gradient Richardson-Romberg Markov Chain Monte Carlo
We illustrate our framework on the popular Stochastic Gradient Langevin Dynamics (SGLD) algorithm and propose a novel SG-MCMC algorithm referred to as Stochastic Gradient Richardson-Romberg Langevin Dynamics (SGRRLD).
High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm
We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)= \mathrm{e}^{-U(x)}/\int_{\mathbb{R}^d} \mathrm{e}^{-U(y)} \mathrm{d} y$.
